Definition 1 For a given set of items I, the set Q of all possible queries associated with item-sets created from I is defined as follows.

i ? I ? i ? Q,

q, q ? Q ? q ? q? Q

These are all.

19

Definition 2 For any query q ? Q, the response set of q, RS(q), is defined as follows

For all atomic i ? Q, RS(i) t?T i?t

RS (q ? q) RS(q) ? RS(q)

20

Definition 3 Let q (i1?i2??ik) and Aq denote the item-set associated with q that is, Aq i1, i2, , ik, the support of Aq is defined as

where q (i1? i2? ? ik).

21

Lemma 1

The support set of Aq SS(Aq), equals to RS(q).

Lemma 2

For queries q, q1, q2 and q3, the following axioms hold

RS(q ? q) RS(q)

RS((q1 ? q2) ? q3) RS(q1 ? (q2 ? q3))

RS(q1 ? q2) RS(q2 ? q1)

22Example

RS((x1 ? x2) ? (x3 ? x2)) RS(x1 ? x2 ? x3)

23

Definition 4

For a given set of items I, the set Q of all possible queries is defined as follows.

i ? I ? i ? Q,

q, q ? Q ? q ? q? Q

q, q ? Q ? q ? q ? Q

q ? Q ? ?q ? Q

24

Definition 5

For any query q ? Q, the response set of transactions, R (q) is defined as

For all i ? Q, RS (i) t?T i?t

RS (q ? q) RS (q) ? RS (q)

RS (q ? q) RS (q) ? RS (q)

RS (?q) T - RS (q)

25Theorem

If q is a transformation of q that is obtained by applying the rules of Boolean algebra, then

RS(q) RS(q)

Each q ?Q can be considered as a generalized itemset. The itemsets investigated in earlier works only consider q ?Q.

26

Lemma 3

RS(q) q ?Q2T

Theorem

(T, 2T, P) is a probability space.

27Rules and Their Response Strengths

Definition 6 The confidence of a rule

Aq ? Aq is defined as

Definition 7 The interest of a rule Aq ? Aq is defined as

Definition 8 The support of a rule Aq ? Aq is defined as

28

Lemma 4 For a rule Aq ? Aq,

Lemma 5 For a rule Aq ? Aq,

29Conclusions

The theory of association mining that is based on a model of retrieval known as the Boolean Retrieval Model has been introduced.

The framework we develop derives from the observation that information retrieval and association mining are two complementary processes on the same data records or transactions.

Based on the theory of Boolean retrieval, we generalize the itemset structure by using all Boolean operators.

30Conclusions (cont.)

By introducing the notion of support of generalized itemsets, a uniform measure for both itemsets and rules (generalized itemsets) has been developed.

Support of a generalized itemset is extended to allow transactions to be weighted so that they can contribute to support unequally.

31Future Work

In order to only generate understandable queries, new restrictions or measures, such as, compactness and simplicity, should be introduced.

(These restrictions or measures could eliminate a large number of frequent generalized itemsets, many of which could have complex structures.)

About PowerShow.com

PowerShow.com is a leading presentation/slideshow sharing website. Whether your application is business, how-to, education, medicine, school, church, sales, marketing, online training or just for fun, PowerShow.com is a great resource. And, best of all, most of its cool features are free and easy to use.

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and
presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!